The invention relates to a transmission system using block-coded or trellis-coded modulations based on a 2-dimensional QAM constellation divided into N sub-sets, and comprising a transmitter and a receiver which is provided with a decoder for decoding said modulations, which decoder comprises a module capable of calculating a distance between each received sample and the point which is closest thereto in each sub-set of the two-dimensional constellation.
Such a decoder renders it possible to decode a sequence of samples received through a channel with noise and resulting from convolutional coding or block coding of a sequence of items of information to be transmitted. The behaviour of a convolutional encoder is described by a trellis in which each transition between two states corresponds to the transmission of one point of the constellation, which is divided into sub-sets such that the distance between two points of a sub-set is greater than the distance which separates two points of the original constellation.
The Viterbi algorithm is known to be an optimum decoding method for convolutional codes. The principle of a Viterbi decoder is described in the article "The Viterbi Algorithm" by G. David Forney, published 3 Mar. 1973 in "Proceedings of the IEEE". Briefly, it may be noted that decoding by means of a Viterbi decoder involves the following three steps:
For each sample of the ing sequence of two-dimensional samples of the recessed signal, that authorized point is to be found which is closest to said sample in each of a series of N sub-sets of the two-dimensional constellation. The branch lengths associated with sample are accordingly calculated on the basis of these N distances. Subsequently, the authorized sequence is to be found which is closest to the sequence of received samples received, i.e. that authorized sequence of which the path length (which is equal to the sum of the branch lengths which make up this path) is smallest.
Finally, the sequence of bits corresponding to the authorized sequence having this shortest path is to be found by means of the trellis.
In principle, the calculation of the branch lengths involves the use of the squared euclidian distance. This calculation of squared values is complicated and requires a high number of bits for its representation. A sufficiently fast memory is not available for certain applications, in particular in the field of hertzian beams where the data rates are very high. It is therefore necessary to simplify the calculation of the branch lengths so as to render possible installations without memory for the Viterbi algorithm. It is known, for example, to use the Manhattan Distance which replaces the sum of squares with a sum of absolute values, as disclosed in the proceedings of the third ECRR (European Conference on Radio Relay systems), edited by Terje Roste and Jonny Normann Skalvik, held in Paris from 17 to 20 Dec. 1991. However, this Manhattan distance has the following disadvantage: when the points received are situated at the boundary of the constellation, the distances thus obtained are subject to errors.